Algebra Examples

$\frac{6 x - 6}{x + 2}$

Step 1

Write $\frac{6 x - 6}{x + 2}$ as an equation.

$y = \frac{6 x - 6}{x + 2}$

Step 2

Find the x-intercepts.

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Step 2.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{6 x - 6}{x + 2}$

Step 2.2

Solve the equation.

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Step 2.2.1

Set the numerator equal to zero.

$6 x - 6 = 0$

Step 2.2.2

Solve the equation for $x$ .

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Step 2.2.2.1

Add $6$ to both sides of the equation.

$6 x = 6$

Step 2.2.2.2

Divide each term in $6 x = 6$ by $6$ and simplify.

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Step 2.2.2.2.1

Divide each term in $6 x = 6$ by $6$ .

$\frac{6 x}{6} = \frac{6}{6}$

Step 2.2.2.2.2

Simplify the left side.

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Step 2.2.2.2.2.1

Cancel the common factor of $6$ .

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Step 2.2.2.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{6}{6}$

Step 2.2.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{6}{6}$

Step 2.2.2.2.3

Simplify the right side.

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Step 2.2.2.2.3.1

Divide $6$ by $6$ .

$x = 1$

Step 2.3

x-intercept(s) in point form.

x-intercept(s): $(1, 0)$

Step 3

Find the y-intercepts.

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Step 3.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{6 (0) - 6}{(0) + 2}$

Step 3.2

Solve the equation.

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Step 3.2.1

Remove parentheses.

$y = \frac{6 (0) - 6}{0 + 2}$

Step 3.2.2

Remove parentheses.

$y = \frac{6 (0) - 6}{(0) + 2}$

Step 3.2.3

Simplify $\frac{6 (0) - 6}{(0) + 2}$ .

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Step 3.2.3.1

Cancel the common factor of $6 (0) - 6$ and $(0) + 2$ .

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Step 3.2.3.1.1

Factor $2$ out of $6 (0)$ .

$y = \frac{2 (3 \cdot 0) - 6}{(0) + 2}$

Step 3.2.3.1.2

Factor $2$ out of $- 6$ .

$y = \frac{2 (3 \cdot 0) + 2 (- 3)}{(0) + 2}$

Step 3.2.3.1.3

Factor $2$ out of $2 (3 \cdot 0) + 2 (- 3)$ .

$y = \frac{2 (3 \cdot 0 - 3)}{(0) + 2}$

Step 3.2.3.1.4

Cancel the common factors.

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Step 3.2.3.1.4.1

Factor $2$ out of $0$ .

$y = \frac{2 (3 \cdot 0 - 3)}{2 (0) + 2}$

Step 3.2.3.1.4.2

Factor $2$ out of $2$ .

$y = \frac{2 (3 \cdot 0 - 3)}{2 \cdot 0 + 2 \cdot 1}$

Step 3.2.3.1.4.3

Factor $2$ out of $2 \cdot 0 + 2 \cdot 1$ .

$y = \frac{2 (3 \cdot 0 - 3)}{2 \cdot (0 + 1)}$

Step 3.2.3.1.4.4

Cancel the common factor.

$y = \frac{2 (3 \cdot 0 - 3)}{2 \cdot (0 + 1)}$

Step 3.2.3.1.4.5

Rewrite the expression.

$y = \frac{3 \cdot 0 - 3}{0 + 1}$

Step 3.2.3.2

Simplify the numerator.

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Step 3.2.3.2.1

Multiply $3$ by $0$ .

$y = \frac{0 - 3}{0 + 1}$

Step 3.2.3.2.2

Subtract $3$ from $0$ .

$y = \frac{- 3}{0 + 1}$

Step 3.2.3.3

Simplify the expression.

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Step 3.2.3.3.1

Add $0$ and $1$ .

$y = \frac{- 3}{1}$

Step 3.2.3.3.2

Divide $- 3$ by $1$ .

$y = - 3$

Step 3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - 3)$

Step 4

List the intersections.

x-intercept(s): $(1, 0)$

y-intercept(s): $(0, - 3)$

Step 5